We say that a graph \(G\)  is \(x\) -far from being \(r\) -partite if \(\chi (G^{\prime })>r\)  for every subgraph \(G^{\prime }\subset G\)  with \(e(G^{\prime })>e(G)-x\) . Balogh, Bushaw, Collares, Liu, Morris and Sharifzadeh [1]} proved that graphs which are \(x\) -far from being \(r\) -partite, contain many cliques of size \(r+1\) .
